All prior art bending processes operate in that two bending tools performing translatory movements carry along the free pin ends and initially bend them into the shape of a C and thereafter a second translatory movement transverse to the first movement, either by the same bending tools or by special lateral bending tools completely closes the C-shaped prebent chain link (e.g. German Offenlegungsschrift No. 21 23 561). However, this process is possible only if the bending tools roll over the surface of the wire pin to be bent or slide on the surface i.e. if relative movement takes place between the contact surface of the bending tool and the wire pin itself. However, this process has the drawback, which previously has had to be accepted, that the surface of the wire pin to be bent is deformed to a significant degree. Since, due to the shortened length of the leg of the remaining portion to be bent, the final bending requires considerable forces, the surface of the wire pin undergoes deformations and damage at precisely that location in the area of the free pin ends which during the subsequent welding process, the welding electrodes will contact. Since the quality of the contact surfaces for the welding electrodes appreciably influences also the quality of the weld (and it is particularly important in the manufacture of chains that link after link the same quality of weld be obtained such partially varying surface deformations have a direct influence on the quality of the weld.